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This popular maths talk gives an introduction to various different kinds of infinity, both countable and uncountable. These concepts are illustrated in a somewhat informal way using the notion of Hilbert's infinite hotel. In this talk, the hotel manager tries to fit various infinite collections of guests into the hotel. The students should lea...
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As taught in 2006-2007 and 2007-2008.
Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions.
This module paves the way by establishing the pri...
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This is a module framework. It can be viewed online or downloaded as a zip file.
As taught Autumn semester 2010.
Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensi...
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This is a module framework. It can be viewed online or downloaded as a zip file.
As taught in Autumn Semester 2009/10
The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing pro...
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The aim of this session is to cover the basic theory of compact linear operators on Banach spaces. This includes definitions and statements of the background and main results, with illustrative examples and some proofs.
Target audience: This material is accessible to anyone who has a basic knowledge of metric space topology, and who kn...
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This is a module framework. It can be viewed online or downloaded as a zip file.
It is as taught in 2009-2010.
This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiatio...
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This is a module framework. It can be viewed online or downloaded as a zip file.
Last taught in Spring Semester 2006
A compilation of fourteen lectures in PDF format on the subject of quantum field theory. This module is suitable for 3rd or 4th year undergraduate and postgraduate level learners.
Suitable for year 3/4 undergraduate and post...
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In June 2009 the Operator Algebras and Applications International Summer School was held in Lisbon. Dr Joel Feinstein taught one of the four courses available on Regularity conditions for Banach function algebras. He delivered four 90 minute lectures on and this learning object contains the slides, handouts, annotated slides and audio podcasts...
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The aim of this material is to introduce the student to two notions of convergence for sequences of real-valued functions. The notion of pointwise convergence is relatively straightforward, but the notion of uniform convergence is more subtle. Uniform convergence is explained in terms of closed function balls and the new notion of sets absorb...
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The aim of this session is to motivate students to understand why we might want to do proofs, why proofs are important, and how they can help us. In particular, the student will learn the following: proofs can help you to really see WHY a result is true; problems that are easy to state can be hard to solve (Fermat's Last Theorem); sometimes st...
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